Robust Cooperative Output Regulation for a Network of Parabolic PDE Systems

TL;DR

This paper develops a robust cooperative output regulation method for a network of parabolic PDE systems using an extended internal model principle and a two-step backstepping design, enabling synchronization despite disturbances and uncertainties.

Contribution

It extends the cooperative internal model principle to infinite-dimensional PDE systems and introduces a systematic backstepping approach for regulator design.

Findings

Successfully applied to a network of four uncertain parabolic agents

Achieves output synchronization with disturbances and model uncertainties

Provides solvability conditions based on communication topology

Abstract

This paper considers the robust cooperative output regulation for a network of parabolic PDE systems. The solution of this problem is obtained by extending the cooperative internal model principle from finite to infinite dimensions. For a time-invariant digraph describing the communication topology, a two-step backstepping approach is presented to systematically design cooperative state feedback regulators. They allow to solve both the leader-follower and the leaderless output synchronization problem in the presence of disturbances and model uncertainty for a finite-dimensional leader. Solvability conditions of the robust cooperative output regulation problem are presented in terms of the communication graph and the agent transfer behaviour. The results of the paper are demonstrated for a MAS consisting of four uncertain parabolic agents with and without a finite-dimensional leader in the presence of disturbances.